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A321912
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Tetrangle where T(n,H(u),H(v)) is the coefficient of m(v) in e(u), where u and v are integer partitions of n, H is Heinz number, m is monomial symmetric functions, and e is elementary symmetric functions.
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24
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1, 0, 1, 1, 2, 0, 0, 1, 0, 1, 3, 1, 3, 6, 0, 0, 0, 0, 1, 0, 1, 0, 2, 6, 0, 0, 0, 1, 4, 0, 2, 1, 5, 12, 1, 6, 4, 12, 24, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 5, 0, 0, 0, 1, 0, 3, 10, 0, 0, 1, 5, 2, 12, 30, 0, 0, 0, 2, 1, 7, 20, 0, 1, 3, 12, 7, 27, 60, 1, 5
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OFFSET
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1,5
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COMMENTS
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The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
Also the coefficient of f(v) in h(u), where f is forgotten symmetric functions and h is homogeneous symmetric functions.
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LINKS
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EXAMPLE
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Tetrangle begins (zeroes not shown):
(1): 1
.
(2): 1
(11): 1 2
.
(3): 1
(21): 1 3
(111): 1 3 6
.
(4): 1
(22): 1 2 6
(31): 1 4
(211): 2 1 5 12
(1111): 1 6 4 12 24
.
(5): 1
(41): 1 5
(32): 1 3 10
(221): 1 5 2 12 30
(311): 2 1 7 20
(2111): 1 3 12 7 27 60
(11111): 1 5 10 30 20 60 20
For example, row 14 gives: e(32) = m(221) + 3m(2111) + 10m(11111).
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CROSSREFS
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This is a regrouping of the triangle A321742.
Cf. A005651, A008480, A056239, A124794, A124795, A215366, A318284, A318360, A319191, A319193, A321854, A321738, A321913-A321935.
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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